As mentioned in the introduction, high-dimensional inference for missing data has been studied in the case of MUCR and we would like to compare our estimators with the corresponding estimators based on a different sample covariance matrix designed for the MUCR case. Under the assumption that \({\rm E}{\mathbf {X}}= 0\)  and each entry of \({\mathbf {X}}\)  is observed independently with probability \(\rho \) , Wainwright [1]} and Lounici [2]} introduced the following substitute of the usual sample covariance matrix
\(\hat{{\mathbf {\Sigma }}}^{\bullet } = (\sigma _{ij}^\bullet )_{1\le i, j\le p}\quad \mbox{with}\quad \hat{\sigma }_{ij}^\bullet = \left\lbrace  \begin{array}{ll}\frac{1}{n(1-\rho )^2}\sum _{k=1}^n X_{ik}^\ast X_{jk}^\ast , & i\ne j \vspace*{10.0pt}\\\frac{1}{n(1-\rho )}\sum _{k=1}^n X_{ik}^\ast X_{jk}^\ast , & i=j\end{array} \right.\) 
